Linear bearing guides are known in which the rolling elements are guided by separate, inter-connected chain links. These re-circulating chains are configured as pull chains. It is also known from a number of patent publications that such a pull chain can be configured as an open or a closed chain. Furthermore, there already exist several patent applications that describe a pull chain not only for a single row of rolling elements but also as double sprocket chains for two re-circulating rows of rolling elements. One such construction is disclosed in the publication EP 0 845 611 A1. This shows a linear rolling bearing of the initially cited type in which an open chain is used on each long side of the guide rail as a guide for two endlessly re-circulating rows of balls. Each chain comprises in its central region situated between the rolling element rows, a flexible connecting strip on whose long sides spacers are arranged spaced behind one another. Rolling elements configured as balls are arranged in the spaces between the spacers. This construction therefore results in the formation of a double row ball chain. However, this chain has drawback that the individual chain links can rupture easily.